In mathematics, an inverse function is known as the anti function. In simple words, it is a function that helps you to reverse the function that is given already. When complicated calculus functions are there, students may find it difficult to calculate their inverse values. But gone are the days when such trouble was massively faced by scholars. Now different sites help you to determine function’s reciprocals instantly. One such site is calculator-online.net that has specifically designed the free online inverse calculator to assist you people in calculating the mirror values of function. What are your thoughts on it?
Let’s get straight to the article below in which we will let you know how to compute function’s mirror entities.
Stay focused!
What is Inverse Function?
In mathematics:
“A particular expression or operation that helps you to invert all parameters or variables of a function is known as the inverse of a function”
Formula:
f (y) = x ⇔ f−1(x) = y
The inverse calculator employs the same equation to find step by step calculations to determine function’s inverse.
Pictorial Representation:
Standard Inverse Function Table:
The inverse function calculator by calculator online helps you to calculate reciprocal of any standard function that originates from the following parent calculus functions:
| Function f(x) | Inverse f −1(y) | Notes |
| x + a | y − a | |
| a − x | a − y | |
| mx | y/m | m ≠ 0 |
| 1/x (i.e. x−1) | 1/y (i.e. y−1) | x, y ≠ 0 |
| x2 | {\displaystyle {\sqrt {y}}} (i.e. y1/2) | x, y ≥ 0 only |
| x3 | {\displaystyle {\sqrt[{3}]{y}}} (i.e. y1/3) | no restriction on x and y |
| xp | {\displaystyle {\sqrt[{p}]{y}}} (i.e. y1/p) | x, y ≥ 0 if p is even; integer p > 0 |
| 2x | lb y | y > 0 |
| ex | lny | y > 0 |
| 10x | logy | y > 0 |
| ax | Log_a y | y > 0 and a > 0 |
| xex | W(y) | x ≥ −1 and y ≥ −1/e |
| Trigonometric Functions | Inverse Functions | various restrictions |
| Hyperbolic Function | Inverse Hyperbolic Function | various restrictions |
How To Calculate Inverse of a Function?
Calculating reciprocal of a function is quite simple and swift with the aid of an inverse calculator. But if your goal comes up with manual calculations, then go through the guide below:
- The first step to consider here is to suppose that the function f(y) has the variable y as independent entity
- After that, you need to check whether x is definable in terms of y or not
- If yes, then it is time to reverse both the variables in the function
- Now the last step that you are left with is to solve for the value of x while dealing with equation y
Resolved Example:
Let us resolve an example here to make your concept more clear:
Statement:
Calculate the inverse of the function given as under:
y = 6x-5
Solution:
Here we have:
y = 6x-5
Solving for x:
Y+5 = 6x
X = y+5/6
Which is the required solution and can also be verified by utilising the inverse calculator.
